HP 48gII Graphing, 50g Graphing manual Transverse Waves 15,1, Longitudinal Waves 15

Waves (15)

Variable	Description
β	Sound level
λ	Wavelength
ω	Angular frequency
ρ	Density of medium
B	Bulk modulus of elasticity
f	Frequency
I	Sound intensity
k	Angular wave number
s	Longitudinal displacement at x and t
sm	Longitudinal amplitude
t	Time
v	Speed of sound in medium (Sound Waves), or
	Wave speed (Transverse Waves, Longitudinal
	Waves)
x	Position
y	Transverse displacement at x and t
ym	Transverse amplitude

Reference: 3.

Transverse Waves (15,1)

Equations:

y = y m ⋅ SIN(k ⋅ x – ω ⋅ t)	v = λ ⋅ f	k =	2 ⋅ π	ω = 2 ⋅ π ⋅ f
			λ

Example:

Given: ym=6.37_cm, k=32.11_r/cm, x=.03_cm, ω=7000_r/s, t=1_s.

Solution: f= 1114.0846_Hz, λ=0.0020_cm, y=2.6655_cm, v=218.0006_cm/s.

Longitudinal Waves (15, 2)

Equations:

s = sm ⋅ COS( k ⋅ x – ω ⋅ t)	v = λ ⋅ f	k =	2 ⋅ π	ω = 2 ⋅ π ⋅ f
			λ

Example:

Given: sm=6.37_cm, k=32.11_r/cm, x=0.03_cm, ω=7000_r/s, t=1_s.

Solution: s=5.7855_cm, v=2.1800_m/s, λ=0.1957_cm, f=1114.08456_Hz.

Equation Reference 559